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Kipish [7]
3 years ago
7

5.) You deposit $5000 into an account compounded annually for 8

Mathematics
1 answer:
Aneli [31]3 years ago
7 0

Answer:

(1- 8 root of 9350/5000 times 100 = -8.14

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Lastima Nelson, Inc. is recruiting a new Chief Financial Officer (CFO). The recruiting budget is $44,000. Lastima has spent $10,
Musya8 [376]
The budget is $44000

Total spent so far is $10000 + $8500 = $18500

The amount left to spend = 44000 - 18500 = $25500

$25500 is the maximum 6% commission that Lastima Nelson Inc. can spend and stays within the budget

Let the maximum price of the home be x
This value of x will be the 100% before the 6% commission is calculated of it.

6% of x is 25500
1% of x is 25500 ÷ 6 = $4250
100% of x is 4250 × 100 = $425,000

So, the maximum value of the home is $425,000
5 0
3 years ago
How to find the vertex calculus 2What is the vertex, focus and directrix of x^2 = 6y
son4ous [18]

Solution:

Given:

x^2=6y

Part A:

The vertex of an up-down facing parabola of the form;

\begin{gathered} y=ax^2+bx+c \\ is \\ x_v=-\frac{b}{2a} \end{gathered}

Rewriting the equation given;

\begin{gathered} 6y=x^2 \\ y=\frac{1}{6}x^2 \\  \\ \text{Hence,} \\ a=\frac{1}{6} \\ b=0 \\ c=0 \\  \\ \text{Hence,} \\ x_v=-\frac{b}{2a} \\ x_v=-\frac{0}{2(\frac{1}{6})} \\ x_v=0 \\  \\ _{} \\ \text{Substituting the value of x into y,} \\ y=\frac{1}{6}x^2 \\ y_v=\frac{1}{6}(0^2) \\ y_v=0 \\  \\ \text{Hence, the vertex is;} \\ (x_v,y_v)=(h,k)=(0,0) \end{gathered}

Therefore, the vertex is (0,0)

Part B:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

\begin{gathered} 4p(y-k)=(x-h)^2 \\  \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}

Rewriting the equation in standard form,

\begin{gathered} x^2=6y \\ 6y=x^2 \\ 4(\frac{3}{2})(y-k)=(x-h)^2 \\ \text{putting (h,k)=(0,0)} \\ 4(\frac{3}{2})(y-0)=(x-0)^2 \\ Comparing\text{to the standard form;} \\ p=\frac{3}{2} \end{gathered}

Since the parabola is symmetric around the y-axis, the focus is a distance p from the center (0,0)

Hence,

\begin{gathered} Focus\text{ is;} \\ (0,0+p) \\ =(0,0+\frac{3}{2}) \\ =(0,\frac{3}{2}) \end{gathered}

Therefore, the focus is;

(0,\frac{3}{2})

Part C:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

\begin{gathered} 4p(y-k)=(x-h)^2 \\  \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}

Rewriting the equation in standard form,

\begin{gathered} x^2=6y \\ 6y=x^2 \\ 4(\frac{3}{2})(y-k)=(x-h)^2 \\ \text{putting (h,k)=(0,0)} \\ 4(\frac{3}{2})(y-0)=(x-0)^2 \\ Comparing\text{to the standard form;} \\ p=\frac{3}{2} \end{gathered}

Since the parabola is symmetric around the y-axis, the directrix is a line parallel to the x-axis at a distance p from the center (0,0).

Hence,

\begin{gathered} Directrix\text{ is;} \\ y=0-p \\ y=0-\frac{3}{2} \\ y=-\frac{3}{2} \end{gathered}

Therefore, the directrix is;

y=-\frac{3}{2}

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Answer: So sorry come back later

Step-by-step explanation:

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2 years ago
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Taletha is preparing for an exam in Algebra II. She knows she will be expected to determine if two functions are inverses of eac
seropon [69]

Answer:

f ○ g(x) = x and g ○ f(x) = x  is the correct composition

Step-by-step explanation:

INVERSE FUNCTIONS: Two functions are said to be inverse of each other if for every y = f(x), there exists a function g(x),

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Now, here if we need to show tha two functions f(x) and g(x) are inverse functions of each other , then show that for every x:

1. f  o g(x)   =   f(g(x))= x

2. g o f(x)  =  g(f(x))   = x

If any two functions satisfy these two conditions, then they are inverse of each other.

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The area of a rectangle is 35 in^2. the length is 7 in. what is the perimeter
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 The perimeter is 24 inches squared
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